NUC In the literature: open

Measuring quark and gluon orbital angular momentum in the proton

In plain words

Quarks and gluons circulate inside the proton, and this circulating motion carries part of its spin. No experiment has yet measured this orbital part directly.

Precise statement

Extract the quark orbital angular momentum $L_q = J_q - \Delta \Sigma_q/2$ with $J_q = (1/2)\,\operatorname{integral} dx\, x\, [H_q(x,0,0) + E_q(x,0,0)]$, where $H$ and $E$ are generalized parton distributions (GPDs, functions encoding both momentum and transverse position of partons) measured in deeply virtual Compton scattering and exclusive meson production, together with the gluon $J_g$. Answer: $L_u, L_d\ \text{and}\ J_g$ at $\mu^2 = 4\,\mathrm{GeV}^2$ with uncertainties below 0.05, satisfying the spin sum rule.

What would settle it

Global GPD extraction from JLab 12 GeV and EIC exclusive data with controlled extrapolation to zero momentum transfer, compared with lattice QCD values.

Status in the literature

Unverified note

Lattice QCD provided values by 2020, but experimental extraction of $E_{q}$, needed for $J_{q}$, remained model dependent as of 2026.